"Donald Trump has kind of started to go wilder and wilder," Kaine told ABC's Martha Raddatz on ABC's "This Week." "He started to make wild claims, kind of scorched-earth claims about the election being rigged ... He shouldn't be engaging in those scare tactics."

Trump has warned supporters that the election is not being conducted fairly, telling a crowd in New Hampshire Saturday, "Remember, it's a rigged system. It's a rigged election. We're gonna beat the rigged system. We're gonna beat the rigged election."

Kaine said that to counter such claims, "We have to keep putting out a message, and we need to call on everybody to speak out about the fact that we run elections and we run them well here ... we're needing to push that message, and we ask the GOP leaders also to stand up for the integrity of the American electoral process."

Republican House Speaker Paul Ryan, for his part, is "fully confident" that the election will be carried out fairly, his spokesperson said Saturday.

"Our democracy relies on confidence in election results, and the speaker is fully confident the states will carry out this election with integrity," Ryan's national press secretary AshLee Strong told ABC News on Saturday.

Kaine also addressed recent sexual-assault accusations against Trump, telling Raddatz the Clinton campaign has absolutely nothing to do with the women coming forward.

Trump has vehemently denied the allegations of assault and threatened legal action against The New York Times for a story giving the accounts of two women making accusations against him.

At a rally in North Carolina on Friday he commented on one of the women -- it was not clear which -- who has made accusations: "When you looked at that horrible woman last night, you said I don't think so. I don't think so."

The GOP nominee also told a crowd of young people at an event in Ohio that, "The Clintons and the corporate media are one in the same ... They collaborate and conspire together," the Los Angeles Times reported.

Kaine said, "It's not because of our campaign, but it's very characteristic of Donald Trump that now he's blaming these women."